Fluid Mechanics_Impact of Jet Vanes_experiment

Ravi Agarwal 09003017 Impact Of Jet Vanes Aim:- The aim of this experiment is to demonstrate the impulse‐momentum theorem as it applies to the impact of a water jet on vanes with different geometrical shapes. This impulse_Momentum theorem is the underlyin g physics behind the operation of the pelton wheel.

Theory:- The jet of water is directed to hit the vanes of a particular shape a force is exerted on the vane by the jet. The amount of force depends on the diameter of the jet shape and the fluid flow rate it also depends on whether the vane is moving or stationary. In this experiment we are concerned about the stationary vane. The force on vane is given by the following formulas: Flat Plate: Ft = ρ a v2 Hemi Spherical: Ft =2 ρ a v2 Where

a = area of jet in m2

ρ = density of water = 1000 kg/ m3 v = velocity of jet in m/s Ft = Force acting parallel to the direction of jet

Impulse-Momentum theorem: The force exerted by the jet on the flat plate (Hemispherical vane) in the direction of jet must be equal to the rate of change of momentum of the jet flow in the same direction.

Apparatus:The experimental setup primarily consists of an arcylic nozzle through which a water jet emerges vert ically in such a way that it may be conveniently observed through a stainless steel enclosure with glass viewports on two sides for visibility. The water jet strikes the target vane positioned above it. The force applied on the vane by the jet can be measured by applying weights to counteract as a reaction force for the impact of jet. Interchangeable arc ylic circular flat plate and a hemispherical cup are provided for the study. Arrangement is made for the movement of the plate and cup under the action of the jet and due to the weight placed on the loading pan. A scale is provided for returning the plate and the cup to their original position i.e. the position before the jet struck the body. A water pump is operated for circulating water to the whole assembly. The water is stored in a tank kept on the ground.

Procedure:1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Sump tank is cleaned and filled with water. (ensure water to be free from foreign bodies) Drain valves are closed and desired vane is placed. Main power supply is switched on.. Pump is switched on and flow rate is set such that the vane is stationary. Flow rate is measured using the measuring tank and stop watch. Flow rate is set again by placing different combination of weights. Flow rate is also measured. All readings are noted. Vane is changed and experiment is repeated. Pump and main supply of power are switched off when experiment is completed. Water is drained from all tanks.

Observations and Calculations:

Data used and recorded: Density of water ρ = 1000 kg/ m3 Diameter of nozzle d = 0.010 m Area of cross section of nozzle A=Πd2 / 4 = 7.85 X 10-5 m2 Area of measuring tank = 0.1 m2 Weight of Aluminum disc + rod = 14.5 gm. Weight of Flat plate disc = 89.5 gm. Weight of hemispherical vane = 97.5 gm.



Sample calculation for Flat plate vane with 98.5 gm weight: Given area of measuring tank = 0.25 x .40 m2 = 0.1 m2 Time = 10 sec Height rise in measuring tank = 6.8 cm = 0.068 m Now, Volume flow rate = Volume / time Volume of fluid = Area x height = 0.1 x 0.068 m3 = 0.0068 m3 So volume flow rate = 0.0068 m3 / 10 sec = 0.00068 m3/ sec Nozzle velocity=0.00068/7.85*10^-5= 8.66m/s Impact velocity= (nozzle velocity2-2*9.8*41.5)(1/2) = 8.18 m/s Force=ϑav2impact = 5.56 N Applying Newton’s second law in the direction of incident jet Force = Mass x Acceleration .

= Mass flow rate x Change in velocity per second

In vertical direction F = Ṁx v = Ṁ x (VcosƟ – V) = ṀV (1-cosƟ) where Ṁ=ϑAV F=ϑAV2(1-cosƟ) For flat vane, Ɵ = 0 and for hemispherical cup Ɵ = 180. 

Constant weights: total = 104 gm for Flat plate and 112 gm for hemispherical vane

Sample weights used = 98.5, 192, 481, 286 gm. Sr..No

Weight external (gm)

1 2 3 4

384.5 286 192 98.5

Sr..No

Weight external (gm)

1 2 3 4

98.5 192 286 384.5

Total weight (gm) 488.5 390 296 202.5

Experimental Force (N)

Height of tank (cm)

4.79 3.82 2.90 1.98

8 7.9 7.8 6.8

Total weight (gm) 202.5 296 390 488.5

Experimental Force (N)

Height of tank (cm)

2.06 2.98 3.90 4.87

5.5 6 6.6 6.7

Flat Plate Vane Q(Volume Nozzle flow rate) Velocity (m3/s) (m/s)

0.0008 0.00079 0.00078 0.00068

10.19 10.06 9.94 8.66

Hemispherical vane Q(Volume Nozzle flow rate) Velocity (m3/s) (m/s)

0.00055 0.0006 0.00066 0.00067

7.01 7.64 8.41 8.54

Height risen (cm)

Impact Velocity (m/s)

Theoretical Force (N)

36.5 35 40 41.5

9.83 9.72 9.53 8.18

7.87 7.68 7.44 5.56

Height risen (cm)

Impact Velocity (m/s)

Theoretical Force (N)

31.7 39.5 35.4 33.3

6.55 7.12 7.98 8.14

7.2 8.54 10.54 10.92

Results and Conclusions:  

The force on the jet for different weights and shape of vanes has been calculated theoretically and observed experimentally. For the hemispherical vane the force is more than that of the flat plate. On increasing the load more jet velocity was required to counter balance the force.

Sources of Errors:     

Error may be introduced due to fluctuating reading of height measuring system. Friction causes error in readings. Tank may be dirty. Error may be introduced due to stop watch use. Error may be introduced due to viscosity effects. Non-uniform flow rate due to fluctuation in power supply of pump.